Construction of stationary quantum states with targeted energies

Abstract

Given an exact stationary state and its energy-eigenvalue, we devise a simple way of generating new families of exact eigenstates with the same eigenenergy, but for different potentials. While this recipe of designing isoergic states is quite general in the context of arriving at new exact solutions from a known premise, relevance of this route with the scheme of construction of isospectral potentials is noted under specific situations. The idea is extended to finding new exact eigenstates with eigenvalues as the sum of energies of two or more separate but known stationary states in dissimilar potentials. Implication of the latter endeavor in the contexts of manifold energy minimization is discussed.